There is so much to address on the subject of finishes and this is not it. Here's some quick and dirty info and general considerations on water vs oil based finishes. Scroll to the bottom for a comprehensive resource.
Visually
The samples below are after a few coats each of General Finishes Arm-R-Seal (top) and water based finish (bottom). If you're looking for a darker, deeper, more rich color in your project, go with an oil based finish. Conversely, if you like the color and figure of the project as is and don't want any color changes happening, use a water based finish.
The first set is Mahogany wood (oil top / water bottom).
This second set is Walnut (oil top / water bottom).
Paint and Bare Wood
A perfect example of when to use water based finish is to put a protective coat over paint.
I used latex paint on the left table, then a few coats of water-based finish as a top coat. The mahogany table on the right was given a few coats of the oil treatment.
Stains
When stain is involved, the oil finish worked nicely on it. The table legs were given one coat of a gel mahogany stain (easier to apply on vertical surfaces) and then a few coats of oil finish. The color darkened very slightly but overall wasn't very noticeable of a change. The Arm-R-Seal vs water finish was also very friendly to apply on a vertical surface.
Over Time
Another consideration is how the color will change over time. An oil based finish with have a slight yellow tint where the water based finish will remain very much the same. This is another great reason for using the water based material over painted surfaces or over anything where the specific color is important to remain constant. Many pieces of furniture use oil based finishes and the color change happens over years and is subtle. If desired, it can always be touched up!
Durability
Water based is thinner than oil based. Most products recommend applying 4-5 coats to get the same effect as 2-3 oil coats.
Project Application
At the risk of providing too little information, depending on what your project is, the water finish might actually be better! This is written with furniture and small crafts in mind. Things change if you're working on floors (high traffic), cooking and eating surfaces (food safe), or even if you are trying to make sure your finish doesn't damage paper in books.
Best of Both Worlds
Do you want the rich color in the wood while having the benefits of water based protection (see book case example)? Apply the oil based finish to your liking and let it fully cure. Then add a few coats of water based finish on top of it.
Sometimes it can take days or weeks for the oil finish to fully cure depending on the weather and humidity, so plan ahead and don't rush the finish!
Thorough Guides
For detailed and easy to read resources, check these books out. (Amazon affiliate links, I do get a small commission from them. Help support this website!)
Understanding Wood Finishing by Bob Flexner - Complete with reference tables, troubleshooting guides, how-tos, and chapter based approach to every aspect of finishing. I read through this before starting each next step in my large table project, mixed with mahogany and painted pine surfaces.
Taunton's Complete Illustrated Guide to Finishing - Same topics written by another master. With similarities and some differences brought from unique perspectives.
Follow me on Instagram @SzaboWoodworks to see how my projects turn out!