Yes, there are huge differences.
Usually, the differences come out in the power supply. I'm not terribly up on solid state, but there's considerable differences in tube amps. The power transformer is usually the biggest expense, often running $100-$200 alone. If you want to use big caps and chokes to smooth the power, you can easily run up to $500-$600 in parts alone. The power supply is key with tubes. Cheap supplies will let "ripple" through that makes the sound output waver a bit. Ditto if you put AC on the filaments instead of DC. The smoother the power and deeper the reserves, the better the sound will be. If you look at the good amps, they all invest heavily in the power supply. You can also run up the tab using tube rectifiers as opposed to diodes.
Next, you have to look at construction. Cheap amps are built on a PCB. That makes them more or less disposable, since a damaged PCB can be a real pain to repair. If traces lift, get broken or scorched, you pretty much have to rebuild the amp entirely, which would cost more than replacing it. The good amps are point-to-point, with terminals and real wires making connections. If something goes wrong in one of those, you can usually get the bad stuff out in short order and repair the amp.
As an example, I'm building Ciuffoli's SESS amp with 417A tubes (plans at Headwize). I paid $700 just for the power transformer, three chokes, and two output transformers. Then I'll spend another $200 for a stepped attenuator volume control, individual terminal points, and I've got another $300 or so in sockets, tubes, jacks, switch, screws, raw aluminum for the case, Teflon wire, and headphone jack. So, about $1,200 in parts, give or take. Since I'm building the case from scratch, it'll probably take 60-70 hours to finish it nicely. This doesn't include a few thousand in tools that I already have.
The rule of thumb is that an amp costs four times its parts if you want to sell it retail. I don't think I could turn a profit on this thing unless I charged about $3,500-$4,000 for it.
This is also why you don't see that many truly high-end tube amps on the market. If you have to add in labor and overhead, it's not easy to break even at the high prices. If you want a really good amp, you often have to build it yourself.