I take it that was just a typo and you have the Spirit 2 speakers as there isn't a Spirit 5 AFAICT.
Your system should have enough resolution to show the difference between the AT and the Rega. Painting in broad strokes then, the Rega should sound more focused, precise, revealing and agile than the AT. It could probably be summed up by saying they have a reputation as sounding lively and musical.
I was going to suggest looking at s/h Planar 3 or P3 as a serious upgrade for similar money, particularly if it comes with something better than the standard supplied cartridge which is almost always the first and biggest upgrade you'll make. However, the prices have gone daft. Even the Pro-Ject Debut and Debut Carbon which were pretty good value on the used market are starting to look pricey compared to new.