I suppose it depends how much of a gaming enthusiast you are.
With Stadia, you'll be missing out on a tonne of next gen games.
Furthermore, Stadia's experience just isn't as good as local gameplay, whichever way you spin it. There's much more latency, so games will often feel a little 'off' even with that 100 mbit connection, and any drops or dips in service quality (on your line directly, or at any point in between yourself and the stadia server) will result in a negative impact on the games visual quality and responsiveness.
As far as playing on your old 1080p TV goes, I don't think you'll miss all that much. At the end of the day, a bump in resolution and colour fidelity affects such a tiny portion of the experience that you take away from playing a video game. I've played plenty of games in 4K or 1080p, and while there's usually a small but noticable difference in visual quality, I'd never really say it affects whether I'm having a good or bad time overall.
The most exciting aspect of next gen systems are the SSDs and faster load times, and overall benefits to performance and graphical fidelity. All of which you'll still benefit hugely from on your older TV. Higher resolution in-game assets will look better on your TV, faster framerates will look more fluid.