These days I don't usually stay in hotels, prefering to have the space that goes with a SC apartment on European trips (even for short breaks) or to do a 'homestay' with a family when in Cuba. That said , when I used to regular do a week away on Tunisia on my own I always stayed in 4* hotels because it usually worked out cheaper! This was because the TOs usually charged a supplement for 'sole use of a double' room in 3* hotels but always had good 'no single supplement' offers for higher grade ones.

For that reason I can't really comment on the difference between a 3* and a 4* there other than that I found a week's HB in a 4* to be cheaper so that's what I went for!
However, having stayed in a range of hotels on one touring trip to Cuba there was a definite difference between the two. Firstly, I never met Cubans staying as guests in 4/5* hotels but I did in the 3* - for me this was a bonus because I at least felt like I was staying in Cuba there and tended not to in the higher rated ones. I found that life in the 4/5* ones was very insulated from local culture daily life. For others this might have been been a drawback of staying in a 3* - it depends on what you are looking for from a holiday.
On the other hand, in the 4/5* hotels, they were clearly used to international guests and the service was usually more attentive - I suspect because staff knew that such visitors could afford to tip more heavily. Don't get me wrong, I'm not saying that the service was poor in 3* hotels, just not so in your face and frankly, more like the more laidback attitude that I think is more typical of most Cuban establishments. Again it depends on what you are looking for.
But probably the biggest difference was in the facilities on offer in the 4/5* ones, bigger, better pools and towels for use around the pool, a better choice of a la carte service to relieve the bordom of the buffets. Bigger, better equipped rooms with a bath and not just a shower in the en-suite and sufficient hot water to fill it. So for most people looking for a beach hotel based holiday then it is probably worth going for at least a 4* or even a 5* one. But you do need to check carefully exactly what is on offer - for example, a lot of the city centre hotels in converted old colonial buildings in places like Havana and Trinidad don't have pools even if they are rated as 5* under the local system.
But for me, overall I preferred the quirkyness of the 3*s and was only needing a clean bed and a decent shower after a day of being out and about. But if I wanted a few days R&R on the beach between city stays in future, Cayo Levisa would win hands down - basic food, basic beach cabin rooms, basic criolla food but an idyllic setting on a white sand beach and loads of peace and quiet with very few people around. Bliss that I'd never find in the 5* Cayo hotels but I can understand why others, particularly families with children would want exactly what such 5* AI hotels can offer.
SM