When I was creating this
website (which works similar to mempool.space and others) I was watching the mempool many times a day. I saw more than once Electrum overestimating fees, suggesting like 100sat/vbyte while you could get a confirmation within a decent amount of time for less than 10 sat/vbyte.
I think mempool.space estimator is better than those native wallet estimators, you just need to understand a little to learn how to use it.
It is designed to do so. If you want to base your fees using the position in the mempool, then there is a mempool option as well and that is approximately the same as any other mempool histograms.
IIRC, Electrum takes the ETA data from the server but can build the mempool histogram. I found it to be quite consistent with Bitcoin Core's which tracks the time it takes for transactions in their mempool to be included in a block and is calculated based on that. While this can resulted in a very conservative fees, it'll take into account block times, intervals, etc and give the user a better chance to hit the estimate.
Mempool.space's priority estimation, I think (maybe I'll take a look at their code in the future, not now) uses the mempool and the estimated transactions that is included in each block. Does it take into account the time elapsed from which the previous block was mined? This results in a far more responsive target but also doesn't average out the irregularities in block intervals. This will strictly be cheaper but it is definitely not as accurate.