Do both. Set up a budget based on what you think will work for you and your desired savings rate. Then track everything you spend and compare it to the budget -- not necessarily daily/weekly, but keep track over time to see how it feels. Does it feel too tight so that you feel stressed or deprived? Is there a particular category you're always struggling to meet? Does the budget feel like a good constraint on impulsive purchases? Then adjust your budget to better suit you -- and check your new savings rate against the chart to see if you are still happy with the time to FIRE.
The idea isn't to hit some artificial savings rate, it's to find a budget and lifestyle that will make both Current You and Future You happy -- not blowing so much now that Future You will curse Current You because you spent so much that he needs to work forever, but also not living like a monk to hit a specified savings rate if that doesn't make you happy and you don't want to live that lifestyle forever. Budgeting and tracking make you conscious of the limits you have imposed on yourself, so that you can weigh the current benefits of each purchase against the future costs in terms of time at work.
Personally, I account for current savings just by knocking the number of years that equates to off the projection. So say your projected FI budget is $30K/yr, and you have $100K saved. If you save 60%, that says 12.5 years if you started from scratch. But since you have $100K saved already, you've got your first 3+ years covered. So really, that takes you down to 9-9.5 years. That's conservative, because it ignores the growth you'll get over that 9-ish years, but the whole savings % is just a ballpark anyway.
The key distinction is that savings % can give you a sense of your time to FI and a good target, but that assumes that you maintain the same income and same future retirement budget as you currently have -- because, as you noted, when you made less money in the past, you might have saved 60% back then, but if your desired lifestyle has inflated, you're not as far along that 12.5-year path as you thought. So if your planned future RE budget is higher than the percent you are currently spending, you will need to save more than what the chart says to hit that target in the same period of time.
If you want more targeted projections, you should look at one of the more detailed calculators people have posted here.