I think both of them satisfy the same goal of measuring the effectiveness of AdWords campaign.
When should one go with one or other? Is there any difference in them at all?
linking to adwords gives you an interface within GA that you can measure inbound traffic directly. it does not necessarily measure conversions which resulted directly from adwords spend. in other words it gives you an overview after which you can setup goals.
After linking Google Analytics and your AdWords manager account, you can:
from the official docs: why link adwords
Link all of the AdWords accounts that you manage to Analytics in one step
Simplify managing your imported Analytics goals and transactions, remarketing lists, and website engagement stats and exported AdWords cost data across multiple AdWords accounts by managing them in one manager account
Automatically link an account to your Analytics properties when you add it to your manager account
Adwords tracking lets you see conversions inside adwords.
from the official docs. why setup goal tracking.
See which keywords, ads, ad groups and campaigns are best at driving valuable customer activity.
Understand your return on investment (ROI) and make better informed decisions about your ad spend.
Use Smart Bidding strategies (such as target CPA, enhanced CPC and target ROAS) that automatically optimise your campaigns according to your business goals.
See how many customers may be interacting with your ads on one device or browser and converting on another. You can view cross-device, cross-browser and other conversion data in your “All conversions” reporting
IMO you should setup both.