I've used both spreadsheets and GnuCash (still do) and can tell you that GnuCash is a suitable system for recording all of your income/expenses/asset/liability information associated with your rental property (and the rest of your personal finances). GnuCash has a good range of configurable reports, so you'll be able to get useful information out of the system when you need it, too.
If you're not already familiar with double-entry accounting systems then you will benefit from doing some homework. GnuCash provides a useful User Manual which includes a primer on double-entry accounting; there are also a number of tutorials available on YouTube and other sources.
GnuCash is configurable to your specific needs. There's no need to record rental income under the generic "other income" account when you can easily create an account called "Rental Income (17 Smith Street)" or whatever name suits you. Ditto for your expense accounts - so you can create different expense accounts for the insurance payments for your home and the insurance payments for the rental property, reflecting their different taxation status.
Having said that, a spreadsheet will still be useful for calculating some of the numbers that should be recorded in GnuCash. And you'll have to make decisions (or seek advice from your accountant) about various things - what is tax deductible and what isn't; should a purchased item be "expensed" in one year or "depreciated" over a number of years; and so on. GnuCash won't make those decisions for you, but it will help you record the information once you've decided what you're going to record.
GnuCash has pros and cons compared to other personal finance packages, but it does provide excellent value for the investment that you put into it!