At the end of the day, 5W-30 or 10W-30 are similar oils once the mower is warmed-up. Full synthetic oil is far superior to any/all conventional motor oils and I use 5W-30 synthetic in all my 4-cycle equipment. In terms of which synthetic oil to choose, all full - not blend synthetic oils can easily handle small engines so I look at price with rebates.
Yes BUT
Water cooled car engine oils are not the same as AIR COOLED mower / Motorcycle oils
next
Mower oils should always be changed at the end of the mower season, before the mower gets laid up over winter.
The quality of the oil is pretty well insignificant, provided it is changed AT THE ENGINE MAKERS REQUIRED INTERVALS and not what is written on the side of the bottle.
Having said that a lot of people use the same oil in all their vehicles & impliments as it saves having 25 different types of oils hanging around which is fine, provided you change it regularly.
And this would mean by hours during the season and also at the end of the season.