Why was the Stark effect discovered much later than the Zeeman effect? This is strange. 
The Zeeman effect involves the magnetic field. The Stark effect involves the electric field. In the course of classical electrodynamics, we get the impression that for many physical processes, the magnetic component of the light field is way less important than the electric component. 
So, why was the Stark effect discovered much later than the Zeeman effect. Actually, it seems that it was much more difficult to confirm the influence of an electric field on an atom after Zeeman's discovery. The famous guy Voigt failed to do so.
Possibly it is more difficult to generate an 'equivalently' strong electric field? But the common impression again is that it is much more difficult to generate a strong magnetic field. 
 A: The discovery of the electron: II. The
Zeeman effect
http://dare.uva.nl/document/2/2775
"Lorentz’s theory was based on the assumption of the
existence of charged vibrating particles inside atoms.
Zeeman’s discovery, together with Lorentz’s theory,
were the first indications of the existence of a new
charged particle, later known as the electron."
Perhaps since the Zeeman effect helped to give rise to the discovery of the electron. And it then follows, a better understanding of the atom would in turn give rise to a better understanding and the implementation of the research to test the Stark effect. 
Way led on to way.
In addition to a more complete understanding of the atom ie the electron's existence. I have to agree with a former post by Yess that earlier experimenters had difficulty maintaining the 100,000 volts per centimeter over an extended period of time needed to complete the Stark spectral line splitting tests.
A: This is hard to answer conclusively but it feels like historical coincidence, coupled with the fact that it is a bit harder to use strong electric fields in a discharge tube without the electrodes sparking. Some points of note:


*

*The Stark effect was discovered after the Zeeman effect, but not very long afterwards: the Zeeman effect in 1897 and the Stark effect in 1913, only 16 years later. This is a long time if the two effects are equally easy to discover, but in absolute terms it's not really that long.

*The discovery of the Zeeman effect would have prompted the community to look for an electric effect, and it seems that it did. Light was known to be electromagnetic so its interaction with matter must be electromagnetic in character. If magnetic fields can influence that interaction, then surely electric fields can do it too.

*However, the conceptual and theoretical underpinnings to solidify this intuition was very shaky during those 16 years. The Bohr model of the atom was published at about the same time that Stark published his findings, and before that, we had very little idea of the structures in matter that were responsible for spectral lines, let alone how they would respond to perturbations. 
This means that for his predictions Voigt had to model the atom as an anharmonic oscillator, which is not a great model. In particular, you need to guess what the scale of the anharmonic terms is, with very little to guide you. This then puts you in a situation where you strongly suspect the effect exists but you have very little idea of how strong it is, and that's not a great place to be in, because it's hard to know whether it will be measurable with the instruments you have available, and whether you're not seeing it because you're doing it wrong or because it's much weaker than you can detect.

*Both Stark and Zeeman were lucky in their choice of gas, in that both sodium and hydrogen have a strong response to the Zeeman and Stark effects respectively. If Zeeman had not been lucky, it's hard to rule out a discovery of electric effects before the magnetic ones - the timespan is really quite short. That said, they probably tried a number of different gases on the run-up to their successful experiments.

*Zeeman was spurred into trying (again) the magnetic-field experiments by the fact that Faraday had also tried them before, which he quite eloquently phrased as

experiments, with negative outcome, performed by great scientists from the past, using worse instruments than are currently available, are worth being repeated.*

If Faraday thought that magnetism could influence light-matter interactions, I'm sure he also suspected electric fields of the same. If Zeeman had been reading those passages instead, would he have persevered until a discovery?
Several of these questions are sort of impossible to answer, but they do raise an alternative reality where for some reason the (harder) Stark effect is detected before the (easier) magnetic-field splitting, and it's not that crazy to get there.
More importantly, though, the electric fields that Stark needed to detect a line splitting were in fact very high, and hard to produce. Stark needed to produce new discharge tubes with special electrodes to maximize the electric field he could apply without the tube sparking, getting to about ten thousand volts per centimeter.** (Zeeman, on the other hand, seems to have worked on an open flame.) This additional load, without the certainty that he would achieve fields high enough to produce splittings, was enough that he needed to do other experiments in the meantime... and the discovery took that much longer to achieve.
In these conditions, then, a 16-year delay between the two effects seems fairly reasonable to me.

References, both of them very readable:


*

*A Simultaneous Discovery: The Case of Johannes Stark and Antonino Lo Surdo. M. Leone et al. Phys. Perspect. 6 no. 3, p. 271 (2004)

*The discovery of the electron: II. The Zeeman effect. A.J. Kox. Eur. J. Phys. 18 no. 3, p.139 (1997).
With a hat tip to StarDrop9 for the second one.
* To temper this out, though, he also seems to have written "One should not communicate to others ideas that have not been worked out yet, plans that have not been carried out yet, experiments that have not been performed yet", which is a valid but somewhat mean view of science.
** It's hard to compare the magnitudes of electric and magnetic fields, but as Michael Seifert notes the linear splittings are of the order of $\mu_BB$ and $ea_0E$, so the magnetic field that produces the same splitting as an electric field $E$ is of the order of $B\sim E/2\alpha c$. For $E\approx10 \:\mathrm{kV}/\mathrm{cm}$, the equivalent magnetic field is $B\approx1\:\mathrm T$, which is definitely much stronger than whatever it is Zeeman used.
