Depends, they are both very different and designs and even in different categories.
Both are designer brands with premium prices and both will always go up in price.
Generally, due to price increases, it hurts the wallet a little less to get the more expensive item first if you love both equally and will end up getting both.
Looking at your pieces I think either would work great!

Spinelli does have that more "different" or "unique" factor compared to Cartier. Even though there has been a bump in interest/popularity, Spinelli is still isn't as well known or as popular as Cartier. Comparing just the two, it is edgier than Cartier.
Highly highly recommend to go to a Spinelli store to try on various sizes, even go in more than once during different times of the day (mid-day vs end of day, etc.). Rings that are designed to be modular and stack/overlap in various ways are always a bit tricky it when it comes to sizing.
I don't have a Spinelli ring but I have the Cartier trinity and even that took quite a bit of trying on. My SA was very thorough in making sure that I got my correct size. Since sizing for these types of rings aren't standard. She wanted to know which hand and which specific fingers I was going to wear my ring. And then she noticed that I was wearing hand lotion when I first started trying on rings, so they felt a tad bit looser or easier to slide on and off. We discussed about my other rings and ring sizes and went back and forth between a few sizes until the fit felt right.
Also, with this design, it's always best if you're able to wear it on more than one finger, just in case your hands swell up a little more on a hot day or towards the end of the day. That way you can switch fingers without the discomfort of a ring that's a tad too tight.
Something else to think about, Spinelli rings are going to take up a bit of space on the sides of your fingers, with those smaller connecting rings, especially if you're going for the design that has more connected rings. Something to keep in mind in relations to comfort and wearing other rings adjacent to it.
If you can go in to take some photos with your regular pieces, it can also give you an idea of how it looks with your current collection and if you like the way it looks.
Seeing that you already have some Cartier in your collection, the love would fit right in. The Spinelli ring would probably fit in with the more simple and industrial look that your Cartier pieces have but it is a different design on its own. So best to be sure!
Though I know there are very few stores in the US.

One in NY one in LA. I think there's a popup store coming in Chicago at the end of this month.