I'd say it's unreasonable (though understandable) to feel any guilt/obligation beyond your contracted/legally required notice projects. Look at the other side - it would be considered unethical for an investor-backed company to keep staff on out of obligation rather than business sense.

As you're interested in working at the other company it probably makes sense to do so - otherwise you may end up resenting your current job for the "what could have been" opportunity. That your obligation to finish your projects is your main doubt reinforces this.

Make sure you have a firm offer from the new company first (you may want to hold off on accepting this offer until you've talked with your current company though), and then have the talk with your current company.

You obviously have no hard feelings towards your current company and enjoyed the opportunity working with them so it's quite likely you'll stay good contacts for down the track. Particularly so if you're able to work something reasonable out for a handover strategy that works for both you and the two companies.

Good luck!