In the episode "Matters of Honor", Delenn was asked to identify a Shadows ship. She later remarked to Sheridan she has never seen one but it fits the descriptions from the Last Great War which occurred thousands of years ago. With technological advancement, how can ships thousand of years ago look similar to ships thousands of years later? Don't the Shadows advance with time? Can you imagine today's Boeing planes looking similar to the first plane made by the Wright brothers 100 years ago?
In addition to Darren's correct answer, one of the themes of Babylon 5 is that the societies of the Vorlons and the Shadows have stagnated. They have spent so long concentrating on winning the galaxy through the actions of the younger races that they no longer focus on much else, so it is plausible that they haven't improved their technology much.
Valorum's comment on your question is also plausible — the Shadows could have hit a technological plateau. While modern aircraft don't look like the Wright Brothers' original flyer, they are actually similar in many ways. And modern aircraft do look substantially similar to aircraft made in the 1950s, 60s, and 70s.
It's also possible that the Shadows simply like the mutant spider-crab look of their ships. Perhaps the technology has improved over the years, but the technology and the appearance are independent. Despite technological improvements, modern passenger aircraft are constrained in appearance by aerodynamic requirements, so they all look broadly similar. If there's no restriction (no need to be aerodynamic in space), the ships can be shaped however they like, and they like that look.
Maybe they even do change the appearance, but the younger races don't notice that shorter or longer legs are in this season because they're too busy being slaughtered. (I'd better post this answer before I get any sillier.)
(Note that this entire answer is somewhat speculative. The first paragraph is drawn fairly closely from what we see and are told in the show, the rest not so much. It should be taken as a supplement to Darren's answer that is drawn entirely from the show itself.)
The Shadows effectively lay dormant for the thousands of years between wars.
It is revealed that
the Icarus awoke the Shadows when it visited Z’ha’dum.
So there wouldn’t have been any technological advancement in the intervening years.
I was going to just comment, but I can't yet...
In his comment, Valorum mentions the concept of technological plateau. Dranon further notes that one of the themes of B5 is that the Vorlons and Shadows have both stagnated. What I wanted to add to this was the connection between these two things, as well as one additional point: The Shadows are repeatedly referred to as "the oldest of the First Ones." This makes them billions of years old. After so long, 2 things will be true:
For a race that is billions of years old, it's highly unlikely there is any further technological advancement available to them. One of the things we note is that while the Vorlons use normal hyperspace jumpoints/jumpgates, the Shadows do not - they simply "shift" in and out of hyperspace without opening jump points. They're way beyond even the Vorlons - even after a few thousand years dormant. There's just no technological room left for them.
And even if there is, they are SO OLD that they are simply going to change very, very slowly. Lorien later says that he was waiting for them on Zha'Ha'Dum for millions of years. These races do not do things quickly, and for such races, even 10,000 years is the blink of an eye. It's reasonable to think that over the few thousand year period we are talking about, they simply haven't changed at all.
May I contribute that AFAIK both Shadows and Vorlons used organic, living ships that didn't rely on technological innovation in a usual sense. It definitely takes more than a thousand years for biological evolution to take place. So, with the masters in hibernation (someone already mentioned it), there would be no way for these ships to change.
This was sort of an obvious explanation ... less obvious would be that neither Shadows nor Vorlons actually wanted to evolve any more themselves. They wanted the younger races to evolve as quickly as possible, so they'd be released from their role as guardians. All they wanted was to join the other "first ones" beyond the rim. Their conflict with each other was about ways to speed up evolution around them!
The answers here are good, but there is something else to consider: the overall goal of the Shadows.
At the end of the day, if the Shadows wanted to just kill everyone, they could do that. They could have whipped out their Death Clouds and went on a rampage across the galaxy way back at the beginning of the series. But they didn't. And not just because the Vorlons would have in turn whipped out their planet killers. It simply wouldn't further their ends.
What the Shadows wanted was to encourage wars, "kick over the ant hills", and so forth. To teach the lower races by getting them to "evolve" to evade destruction.
Past a certain point, being that kind of force simply doesn't require improvements in technology. So long as you have weapons that can one-shot the enemy's best ships, you're doing OK. If the younger races have become stronger, just add more ships.
And if things go sideways, you always have those Death Clouds to fall back on...