The SFX in T1 looked wrong to me when it came out, and are very hard to watch today, whereas T2 was pretty much flawless and still looks good. So money well spent.
However, there more differences than the budget. T1 is basically an extended chase sequence. Although it introduces a lot of the SF ideas of the franchise, it doesn't have much moral depth. What we initially take to be a man is gradually revealed to be a machine. And, well, chase chase chase. There's nothing to it.
T2 has some chase sequences in it, but also a long middle section in which they stop, take stock, and then go on the offensive, gunning for the scientist and then for the labs. It has several moral twists, such as over whether Sarah will or should kill the scientist. What we initially know to be a machine gradually becomes more human. It is a much richer story. Some of the issues which are now being explored in the TV series, such as the contradiction between teaching John how to be a future leader and preserving him so he has a future, are already fully developed in the film.
So for me the second film is far more than a remake, and is much better than the first.