Let's start with some basics. Both games are designed for small warbands, around 30 to 50 figures per side I would say, depending on your chosen force. You can play on a smallish table, Saga in particular recommends 4x3, while Dragon Rampant makes no stipulation but from experience you can play on a typical dining table of 5x3. Both systems are easy to learn and after a handful of games you probably won't need the rulebook too much. Games will typically last an hour or so, once you are up to speed.
Dragon Rampant uses an activation system. Each unit has a score from 5 to 7 it has to equal or exceed on 2 dice to either move, shoot or attack. If a unit fails to activate because you roll under the activation score, your turn ends and your opponent takes a turn. Assuming you are successful and attack (say), you roll 12 dice (or 6 if your unit is at half strength or lower), with a score needed to hit the enemy, between 3 for the best troops and 6 for the worst. You then take the number of hits, divide by your opponent's armour and arrive at a number of casualties for your enemy. Combat is simultaneous, so your opponent does the same. Any side taking casualties tests morale, again a simple 2d6 roll, with deductions for each casualty suffered in the unit to date, comparing it to a morale value. You might pass with no effect, retreat and get battered (shaken) or rout. That's the game in a nutshell.
Saga has less profiles! There are just four troop types in the basic game - Warlord, elite, regular and levy. The warlord is free, then you pay one point to hire 4 elite or 8 regular or 12 levy troops. The standard game size is 6 points, so you could have just 24 elite troops, or 72 levy, at the two opposite ends of the spectrum. Typically you will have about 40 troops. Once bought, you can field your troops in units of from 4 to 12. Each unit on the battlefield (not levy) generates a Saga dice, while your warlord generates two Saga dice. Having rolled the Saga dice you place them on a battle board, to determine which of your units are activated and any special features or powers they will use. These battle boards are designed to emulate different play styles - Vikings are aggressive with many combat bonuses, Danes are more defensive, Welsh are more of a skirmish force. There is an excellent primer that explains the basics far better than I could.
detailed in this original post. There are additional troops types to cover beasts, war machines and a very basic magic system. The mod originally contained boards for Dwarves, Undead, Wild Tribes (chaos) and Elves, with newer boards for orcs and dark elves, plus plans for more. The battle boards in the free download will give you a very good idea of the kind of thing that the game aims to achieve.
The original set of Saga rules is not as cheap as Dragon Rampant, nor is it available in electronic format, but unfortunately you need a copy to understand the basic rules. Note that you need the original rule set, not one of the expansions. There is a newer version set in the Crusade era, though the rules are the same - it's more Saga version 1.1 than anything - from various reviews I have read this is an excellent book, but higher priced than the original dark ages book.