The metrics of different routing protocols are not compatible, and you need to assign a metric when redistributing from one to the other. Use metrics which make sense for you network design so that the path chosen by your routers will be your preferred path. Remember that lower metrics are preferred over higher metrics.
You can run into problems with mutual redistribution where routes get redistributed back and forth between your routing protocols. A way to avoid this problem is to use route tags. Then you can deny routes that have been redistributed from one protocol to another, and back again.
Cisco has documents regarding this, and you can search for them. For example, Redistributing Routing Protocols:
When you redistribute one protocol into another, remember that the metrics of each protocol play an important role in redistribution.
Each protocol uses different metrics. For example, the Routing
Information Protocol (RIP) metric is based on hop count, but Interior
Gateway Routing Protocol (IGRP) and Enhanced Interior Gateway Routing
Protocol (EIGRP) use a composite metric based on bandwidth, delay,
reliability, load, and maximum transmission unit (MTU), where
bandwidth and delay are the only parameters used by default. When
routes are redistributed, you must define a metric that is
understandable to the receiving protocol.
Redistribution Configuration Syntax and Examples
IGRP and EIGRP
This output shows an IGRP/EIGRP router redistributing static, Open
Shortest Path First (OSPF), RIP, and Intermediate
System-to-Intermediate System (IS-IS) routes.
router igrp/eigrp 1
redistribute ospf 1
default-metric 10000 100 255 1 1500
IGRP and EIGRP need five metrics when redistributing other protocols:
bandwidth, delay, reliability, load, and MTU, respectively.
This output shows an OSPF router redistributing static, RIP, IGRP,
EIGRP, and IS-IS routes.
router ospf 1
network 220.127.116.11 0.0.255.255 area 0
redistribute static metric 200 subnets
redistribute rip metric 200 subnets
redistribute igrp 1 metric 100 subnets
redistribute eigrp 1 metric 100 subnets
redistribute isis metric 10 subnets
The OSPF metric is a cost value based on 10^8/bandwidth of the link in
bits/sec. For example, the OSPF cost of Ethernet is 10: 10^8/10^7 = 10
Note: If a metric is not specified, OSPF puts a default value of 20 when redistributing routes from all protocols except Border Gateway
Protocol (BGP) routes, which get a metric of 1.
When there is a major net that is subnetted, you need to use the
keyword subnet to redistribute protocols into OSPF. Without this
keyword, OSPF only redistributes major nets that are not subnetted.
It is possible to run more than one OSPF process on the same router.
However, running more than one process of the same protocol is rarely
needed, and consumes the router's memory and CPU.
You do not need to define metric or use the default-metric command
when redistributing one OSPF process into another.